Atmospheric flows is a representative
example of turbulent fluid flows.The model is based on the concept that
spatial integration of enclosed small scale (turbulent eddy) fluctuations
result in organized large eddy circulations. The eddy energy spectrum therefore
follows statistical normal distribution characteristics according to the*
Central Limit Theorem*. Therefore, the square of the eddy amplitude,
i.e., variance represents the statistical normal probability density distribution.Such
a result that the additive amplitudes of eddies, when squared, represent
probability densities is observed in the sub-atomic dynamics of quantum
systems such as the electron or photon. Atmospheric flows therefore follow
quantumlike mechanical laws. The root mean square (r.m.s) circulation speed
** W**
of large eddy of radius

(1)

*E=Hn _{R}*

(2)

where The relative phase angle between large and turbulent eddies is equal to

(3)

Equation(3) is analogous
to *Kepler's third law of planetary motion*, namely, the square of
the planet's year (period) to the cube of the mean distance from the *Sun*
is the same for all planets and results in inverse square law analogous
to the* Newton's inverse square law for gravitation*. The model
is similar to a superstring model for subatomic dynamics [M. Kaku,

**WAVE-PARTICLE DUALITY IN CLOUD FORMATION**

The apparent paradox
of wave-particle duality in microscopic scale quantum systems is however
physically consistent in the context of macroscale atmospheric flows since
the bi-directional energy flow structure of a complete atmospheric eddy
results in the formation of clouds in updrafts regions and dissipation
of clouds in downdrafts regions.The commonplace occurrence of clouds in
a row is a manifestation of wave-particle duality in the macroscale quantum
system of atmospheric flows. The above-described analogy of quantum-like
mechanics for atmospheric flows is similar to the concept of a subquantum
level of fluctuations whose space- time organization gives rise to the
observed manifestation of subatomic phenomena, i.e., quantum systems as
order out of chaos phenomena [G.Grossing, *Il Nuovo Cimento* **103B**
(1989) 497]. H. E. Puthoff [*Phys. Rev.A*. **39**, 2333 (1989)]
has also put forth the concept of *"Gravity as a zero-point fluctuation
force" *( Quantum
fluctuations of empty space ).The vacuum zero-point fluctuation (electromagnetic)
energy manifested in the *Casimir* effect is analogous to the turbulent
scale fluctuations whose spatial integration results in coherent large
eddy structures.